Geometry

Solids

Easy

Two cubes have their volumes in the ratio 1:27. The ratio of their surface areas is?

1:9

3:7

2:5

1:10

✅ Correct Option: 1

Volumes are in the ratio $1:27$ , so the sides are in the ratio $1:3$ (cube roots).

Surface areas vary as the square of the side, so the ratio is $1^2 : 3^2 = 1:9$ .

2026: 22 May Shift 2

If the diagonal of a cube is $8\sqrt{3}$ cm then the volume of cube is :

2026: 14 May Shift 2

Consider the surface area of the following solids.

A. A cube of edge 4 cm.

B. A cylinder with a diameter of base 14 cm and height 35 cm.

C. A hemisphere with 28 cm diameter.

D. A sphere with a radius of 7 cm.

Arrange the above in decreasing order and choose the correct answer from the options given below:

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Find the surface area of a sphere of radius 10.5 cm?

2023: 5 June Shift 2

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).

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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

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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?

Two cubes have their volumes in the ratio 1:27. The ratio of their surface areas is?

Solution

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