CUET General Test Geometry > Solids PYQs

Match List-I with List-II | List-I | List-II | |---|---| | (Shapes) | (Area/Perimeter/Diagonal/slant height) | | (A) Trapezium | (I) √(l² + b² + h²) | | (B) Sector of a circle | (II) √(R² + (R - r)²) | | (C) Cuboid | (III) 1/2 h(a + b) | | (D) Frustum of cone | (IV) (θ/360°) × 2πr | Choose the correct answer from the options given below:

A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively. What is the volume of clay required for making a tile?

Consider the surface area of the following: (A) A cube having each side as 6 cm. (B) A cylinder with a diameter of base 14 cm and length 80 cm. (C) A cone of diameter 14 cm and a slant height of 10 cm. (D) A sphere of radius 10.5 cm. The surface area of these in decreasing order are: Choose the correct answer from the options given below:

The ratio of the diameter and height of the right circular cylinder is 4 : 3. If the diameter of the cylinder is reduced 25 %, then its total surface area is reduced to 318.5π m². What is the circumference of the base of the cylinder?

If a cone and sphere have equal radii and volumes, then determine the ratio of the diameter of the sphere to the height of the cone?

If the ratio of the radii of the sphere and hemisphere is √3:2, then determine the ratio of their total surface area?

A solid, metallic right circular cone of radius 7 cm and height 3 cm is melted into three cubes. If the sides of two cubes are 3 cm and 5 cm, then the side of the third cube will be how much?

A solid sphere of radius 15 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 9 cm and its height is 100 cm, find the uniform thickness of the cylinder.

A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into another right circular cylindrical flask whose radius is two-third of the radius of base of the circular cone. Then, the height of the tea in the cylindrical flask is

The ratio of the radius and height of a cone is 3:4. Its volume is $37\frac{5}{7}$ cm³. The slant height of the cone is

If the length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid

If a metallic rod of 10 cm length and 2 cm radius is stretched into a wire of 40 m length having uniform thickness, then find the radius of the stretched wire.

If the slant height of a cone is decreased by 15 percent and the radius of its base is increased by 20 percent, then by what percent will its curved surface area change?

A sphere of maximum volume is 'cut out' from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut-out sphere is:

A right circular metal cone (solid) is 42 cm high and its radius is $\frac{21}{2}$ cm. It is melted and recast into a sphere. Then the radius of the sphere will be:

If the areas of adjacent faces of a cuboid (rectangular prism) are in the ratio of 2: 3: 5 and its volume is 900 cm³, then the length of the longest side is

If the radius of a sphere is increased by 50%, find the percent increase in surface area.

How many meters of cloth 6 metre wide will be required to make a conical tent, the radius of whose base is 21m and height is 20m?

Find the values and arrange in increasing order: (A) If each edge of a cube is increased by 20%, then the percentage increase in its volume is: (B) If the radius of a cylinder is increased by 20%, while height increase 10%, then the percentage increase in the volume of the cylinder (C) If each edge of a cube is increased by 20%, then the percentage increase in its surface area is: (D) If the radius of a sphere is increased by 10%, then the percentage increase in its volume is: Choose the correct order:

The areas of three adjacent faces of a cuboidal box are 96 cm², 48 cm² and 72 cm², respectively. The volume of the box is

The base radius of a cone is 21 cm and the height is 28cm, then which of the following is/are correct? (A) Slant height = 35 cm (B) Slant height = 33 cm (C) Volume = 12936 cm³ (D) Curved Surface Area = 2310 cm² Choose the correct answer from the options given below:

In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same diameter and the same height?

Three spherical balls of radius 2 cm, 4 cm, and 6 cm are melted to form a new spherical ball. In this process, there is a loss of 25% of the material. What is the radius (in cm) of the new ball?

A cylindrical jar having a base of radius 15 cm, is filled with water up to a height of 20 cm. If a solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in the water, then the increase in the level of water is:

The ratio of radii of two right circular cylinders (A and B) is 2:3. The ratio of volumes of the cylinders A and B is 9:7, then what is the ratio of the heights of the cylinders A and B?

$V_1, V_2, V_3$ and $V_4$ are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4x cm respectively. The following statements regarding these volumes are given below. (A) $V_1 + V_2 + 2V_3 < V_4$ (B) $V_1 + 3V_2 > V_3 + V_4$ (C) $2(V_1 + V_3) + V_2 = V_4$ (D) $V_1 + 4V_2 + V_3 < V_4$ Which of these statements is/are correct? Choose the correct answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | (Figures, etc.) | (Area/Volume/Diagonal etc.) | | (A) Surface area of Cube | (I) $\pi(R^2 - r^2)$ | | (B) Volume of Right pyramid | (II) $a\sqrt{2}$ | | (C) Area of Circular Ring | (III) $6a^2$ | | (D) Diagonal of Square | (IV) $\frac{1}{3}$(area of base) × height | Choose the correct answer from the options given below:

Consider the following statements: I. If the height of a cylinder is doubled, the area of the curved surface is doubled. II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. Which of the above statement(s) is / are true:

Consider the volumes of the following: (A) A cylinder with a radius of base 7 cm and height 10 cm. (B) A cone of radius 7 cm and height 9 cm. (C) A sphere of radius 6 cm. The volumes of these figures in decreasing order shall be: Choose the correct answer from the options given below:

Match the given areas of various solid objects with their respective formulae: | List I | List II | |---|---| | Area of solid object | Formula | | (A) Lateral surface area of a cylinder | (I) $\pi r\sqrt{r^2 + h^2}$ | | (B) Total surface area of a hemisphere | (II) $4\pi r^2$ | | (C) Lateral surface area of a cone | (III) $2\pi rh$ | | (D) Surface area of a sphere | (IV) $3\pi r^2$ | (Where, r = radius of the solid shape (or base) and h = height of the solid shape.) Choose the correct answer from the options given below:

Consider the following statements: I. If the height of a cylinder is doubled, the area of the curved surface is doubled. II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. Which of the above statement(s) is / are true:

Which of the following statements are true?<br/><br/>(A) If the diagonal of a cube is $6\sqrt{3}$ cm, then its volume and surface area are equal.<br/><br/>(B) If a rectangular block having dimensions 6 cm x 12 cm x 15 cm is cut into an exact number of equal cubes, then the least possible number of such cubes is 27.<br/><br/>Choose the correct answer from the options given below:

Read the information given carefully and answer the question that follows: $$\newline$$ (A) 72 kmph = 20 m/s $\newline$ (B) 25 m/s = 80 kmph $\newline$ (C) Total Surface area of a Cube of edge length $a$ is $6a^2$ $\newline$ (D) Volume of a Cube of edge length $a$ is $a^3$ $$\newline$$ Choose the correct answer from the options given below:

The base diameter of a cylinder is 21 cm and the height is 28 cm, then: (A) Radius of cylinder = 10.5 cm (B) Volume = 12936 cm³ (C) Curved Surface Area = 1848 cm² (D) Total surface area = 2541 cm² Which of the following is/ are correct? Choose the correct answer from the options given below:

The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²):

A cone of height 24 cm and base radius 6 cm is made of modelling clay. A child reshapes it in the form of a sphere. The radius of the sphere is :

A well has to be dug out 20 m deep and its radius is 3.5 m. Find the cost of plastering the inner curved surface at Rs 5 per square meter.

Which of the following statements are incorrect? (a) Volume of a cone = $\frac{1}{3}\pi r^3 h$ (b) Volume of a cone = $\frac{1}{3}\pi r^2 h$ (c) Volume of a hemisphere = $\frac{2}{3}\pi r^2$ (d) Volume of a hemisphere = $\frac{2}{3}\pi r^3$ (e) Volume of a cylinder = $\frac{1}{3}\pi r^3 h$ Choose the correct answer from the options given below:

The surface area (in $m^2$) of a sphere of radius 7 cm is: Use $\pi = \frac{22}{7}$

The volume of a sphere of radius r is obtained by multiplying its surface area with:

From a solid cylinder whose height is 2.4 cm and diameter is 1.4 cm, a conical cavity of same height and same diameter is carved out. The total surface area of the remaining solid is: Use $\pi = \frac{22}{7}$

The heights of two right circular cones are in the ratio 1 : 2 and the circumferences of their bases are in the ratio 3 : 4. Find the ratio of their volumes.

A solid metallic sphere of radius 8 cm is melted and recasted as a cone of height 8 cm. Find the base radius of the cone (in cm).

A toy is made in the shape of a hemisphere of diameter 7 cm surmounted by a cone. If this 15.5 cm high toy is polished at 20 paise per cm$^2$, then find the cost of polishing. Take $\pi = \frac{22}{7}$

The volumes of 3 solid cubes made of metal are 125 cm$^3$, 64 cm$^3$ and 27 cm$^3$ respectively. After melting all the three cubes a solid cube is made. Find the edge of the new cube.

A sector as shown in the figure is assembled to form a cone. What is the base radius (in cm) of the cone so formed ? $\left(\pi = \frac{22}{7}\right)$<img src="https://balti.afterboards.in/RXIU9wtZH3egbaH" width="300px"/>

The curved surface area of a right circular cylinder of height 14 cm is 88 cm$^2$. The diameter of the base of the cylinder is $\left(\text{Use } \pi = \frac{22}{7}\right)$ :

64 small solid iron spheres of radius 'r' are melted to form a big sphere of radius R. If S and S' are surface areas of the small and the big sphere respectively, then find the ratio S' : S.

Radius of the base and height of a cone are 5 cm and 12 cm respectively. Find its slant height.

A cuboidal slab of copper having dimensions 22 cm $\times$ 10 cm $\times$ 5 cm is melted and recasted in the form of a wire of 1 mm diameter. The wire is rubber coated at the rate of Rs. 1.50 per meter. Find the cost of rubber coating (in Rs.) Use $\pi = \frac{22}{7}$.

The area of four walls of a rectangular hall having length 18 m and height 8 m is 448 m$^2$. What is the breadth of the hall (in m)?

64 solid iron spheres of radius r are melted to form a sphere of radius R. Find R : r.

If each side of a cube is reduced by 50%, the surface area will reduced by.

If the volume of a cube is 27 cm^3, then the diagonal of cube is

Charge of cellophane paper is Rs. 40 per kg. How must expenditure would be there to cover a cube of edge 25 cm with a cellophane paper, if one kg of paper covers 50 sq.cm. area?

If the edge of a cube is 15 cm, then the volume of a cube is :

A right angle triangle is rotated along the base. If the perpendicular, hypotenuse and base of the triangle are 8 cm, 10 cm and 6 cm respectively. Find the volume of the cone formed through rotation. ($\pi = 3.14$)

In a swimming pool measuring 80 m x 60 m, 120 men take a dip. If the average displacement of water by a man is 6 m$^3$, then the rise in water level is -

A volume of a wall is 128 cm$^3$. If the height of the wall is 6 times its breadth and the length is 9 times its breadth, find the breadth.