# Surface Areas And Volumes - Class 9 - Mathematics

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## Extra Questions - Surface Areas And Volumes | NCERT | Mathematics | Class 9

The curved surface area of a cylinder is $2200 \mathrm{sqcm}$, and the circumference of its base is $220 \mathrm{~cm}$. Then the height of the cylinder is:

A) $2.2 \mathrm{~cm}$

B) $5 \mathrm{~cm}$

C) $22 \mathrm{~cm}$

D) $10 \mathrm{~cm}$

The correct option is **D**: $ 10 , \text{cm} $

Details:

The

**circumference of the base**of the cylinder is given by: $$ 2 \pi r = 220 , \text{cm} $$The

**Curved Surface Area (CSA)**of the cylinder is defined as: $$ 2 \pi r h = 2200 , \text{cm}^2 $$Given the circumference, the formula can be rearranged to find the height ($ h $): $$ 220 , \text{cm} \times h = 2200 , \text{cm}^2 $$ $$ \Rightarrow h = \frac{2200}{220} , \text{cm} $$ $$ \Rightarrow h = 10 , \text{cm} $$

Thus, the height of the cylinder is **10 cm**.

A room is 15 feet long and 12 feet broad. A mat has to be placed on the floor of this room leaving $1 \frac{1}{2}$ feet space from the walls. What will be the cost of the mat at the rate of Rs. 3.50 per square feet?

A) Rs. 378 B) Rs. 472.50 C) Rs. 496 D) Rs. 630 E) None of these

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The surface area of a solid metallic sphere is $2464 \mathrm{~cm}^{2}$. It is melted and recast into solid right circular cones of radius $3.5 \mathrm{~cm}$ and height $7 \mathrm{~cm}$. Calculate the number of cones recast.

A) 256

B) 128

C) 64

D) 32

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A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find the diameter of the sphere.

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A solid metallic cone of radius $12$ cm and height $48$ cm was recast into a sphere. The radius of the sphere is

(A) $24$ cm

(B) $12$ cm

(C) $74$ cm

(D) $15$ cm