# Surface Area of a Frustum

## Trending Questions

**Q.**Question 7

The curved surface area of a frustum of a cone is π(r1+r2)l, where l=√h2+(r1+r2)2 r1 and r2 are the radii of the two ends of the frustum and h is the vertical height.

**Q.**

A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.

**Q.**

A tent is made in the form of a frustum of a cone surmounted by another cone. The diameters of the base and the top of the frustum are 20 m and 6 m respectively, and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required. [Take π=22/7.]

**Q.**In fig. 5, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs 500/sq. metre. (Use π=227)

**Q.**

A rectangular tank with a square base, an open-top, and a volume of $864$ ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let $\mathit{\text{s}}$ be the length of one of the sides of the square base and let $\mathit{\text{A}}$ be the surface area of the tank. Write the objective function.

**Q.**

The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.

**Q.**The height and radius of the cone of which the frustum is a part are h

_{1}and r

_{1}respectively. If h

_{2}and r

_{2}are the heights and radius of the smaller base of the frustum respectively and h

_{2}: h

_{1}= 1 : 2, then r

_{2}: r

_{1}is equal to

(a) 1 : 3

(b) 1 : 2

(c) 2 : 1

(d) 3 : 1

**Q.**

The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its capacity and total surface area. [Use π=3.14.]

**Q.**

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per m2 . (Note that the base of the tent will not be covered with canvas).

**Q.**

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs 15 per 100 cm2. [Use π=3.14.]

**Q.**

The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area. [Use π=3.14.]

**Q.**

Derive the formula for the curved surface area and total surface area of the frustum of cone.

**Q.**

A bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs 20 per litre and the cost of metal sheet used if it costs Rs 10 per 100 cm2 [Use π=3.14.]

**Q.**

A reservoir in the form of the frustum of a right circular cone contains 44 × 107 litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir. (Take : π = 22/7)

**Q.**

The slant height of a bucket is 45 cm and the radii of its top and bottom are 28 cm and 7 cm respectively. The curved surface area of the bucket is

(a) 4953 cm2 (b) 4952 cm2 (c) 4951 cm2 (d) 4950 cm2

**Q.**If r

_{1}and r

_{2}denote the radii of the circular bases of the frustum of a cone such that r

_{1}> r

_{2}, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.

**Q.**In the given figure, a hollow cone is cut by a plane parallel to the base. If the curved surface area of the frustum obtained is 8 times of the curved surface area of the smaller cone obtained, then which of the following is true?

- r2=9r1

- r22=3r21

- r2=3r1

- 3r22=r21

**Q.**

The radii if the circular ends of a bucket of height $24cm$ are $15cm$and $5cm$. Find the area of its curved surface.

**Q.**

The height of a cone is 8 cm and its base radius is 6 cm. Find the curved surface area the cone. (Use π = 3.14).

**Q.**

A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs.10 per 100 cm2. (Use π = 3.14).

**Q.**

A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find

(i) the volume of water which can completely fill the bucket;

(ii) the area of the metal sheet used to make the bucket.

**Q.**The diameters of the ends of a frustum of a cone are 32 cm and 20 cm. If its slant height is 10 cm, then its lateral surface area is

(a) 321 π cm

^{2}

(b) 300 π cm

^{2}

(c) 260 π cm

^{2}

(d) 250 π cm

^{2}

**Q.**Question 3

A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

**Q.**

A circular ground of radius 50 m has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is 625 πm2, then the height of the tent is____cm.

90.42

96.8

88.5

100.6

**Q.**A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the tank

**Q.**The radii of the ends of a frustum of a cone of slant height l are r1 and r2. The curved surface area of the frustum of the cone is

- 2πl(r1+r2)
- πl(r1+r2)
- πl(r21+r22)
- πl(r1−r2)

**Q.**Water is flowing at the rate of 10 cm/minute through a pipe of diameter 10 cm into an empty bucket, which is in the form of frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Then, the time in which the level of water in the bucket will rise 15 cm, is 1. √17/10 minutes 2. √19/5 minutes 3. √17/5 minutes 4. √19/10 minutes

**Q.**Question 8

Write ‘True’ or ‘False’ and justify your answer in the following

An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder

**Q.**The slant height and height of a frustum of a cone are 5 cm and 4 cm respectively. If the circumference of one of its ends is 44 cm, then the radius of the other end can be

- 3 cm
- 5 cm
- 8 cm
- 10 cm

**Q.**The curved surface area of the frustum of a cone is 48cm2. If the perimeters of circular ends are 18 cm and 6 cm, then its slant height is

- 6 cm
- 4 cm
- 5 cm
- 8 cm