EASY
Earn 100

If it takes 173.25 sq cm of sheet to make a hemispherical bowl, then write the length of the diameter of the forepart of the bowl.

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Important Questions on Surface Areas and Volumes

HARD
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm. Find the total surface area of the article.
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MEDIUM

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig.). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

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MEDIUM
The decorative block shown in the figure is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. The total surface area of the block is 
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MEDIUM
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
MEDIUM

Match the following:

Volume of a cone 2πrh
Volume of a frustum 3πr2
Total surface area of a cone 23πr3
Total surface area of a hemisphere lbh
Volume of a cuboid πrl
Lateral surface area of cylinder 2πrr+h
Surface area of a sphere 13πr2h
Volume of hemisphere πrr+l
Curved surface area of cone 4πr2
Total surface area of a cylinder 13πhR2+r2+Rr

 

 

MEDIUM
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.useπ=227
MEDIUM
The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint 1 cm2 of the surface is  0.05. Find the total cost to painting the vessel all over.
HARD
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.
MEDIUM
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 500 per m2. (Note that the base of the tent will not be covered with canvas.) 
MEDIUM
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5:12, write the ratio of the total surface area of the cylinder to that of the cone.
EASY
The radii of two cylinders are in the ratio 3:5 and their heights are in the ratio 2:3. What is the ratio of their curved surface areas?
HARD
A room is 8.5 m long, 6.5 m broad and 3.4 m high. It has two doors, each measuring 1.5 m by 1 m and two windows, each measuring 2 m by 1 m. Find the cost of painting its four walls at 160 per m2.
MEDIUM
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
MEDIUM
An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. (Use π=22/7)
HARD

An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see Fig.).

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MEDIUM
A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces ?
MEDIUM
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
EASY

Figure 1 below is a solid cuboid made of unit cubes. Figure 2 is obtained after removing some unit cubes from figure 1.

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Based on the figures shown above, the surface area of the cuboid in figure 1 is _____ the surface area of the solid in figure 2.

MEDIUM

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

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MEDIUM
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.