CUET General Test: GeometrySolids. Free, no login required.

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:

(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?

(A) If the diagonal of a cube is $6\sqrt{3}$ cm, then its volume and surface area are equal.

(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.

Choose the correct answer from the options given below:

Read the information given carefully and answer the question that follows:

(A) 72 kmph = 20 m/s

(B) 25 m/s = 80 kmph

(C) Total Surface area of a Cube of edge length $a$ is $6a^2$

(D) Volume of a Cube of edge length $a$ is $a^3$

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 ? $\left(\pi = \frac{22}{7}\right)$

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