Surface Areas and Volumes — Class 10 solved problems

17 problems from this chapter, each solved step by step.

A playing top (lattu) is shaped like a cone surmounted by a hemisphere. The total height is 5 cm and the diameter is 3.5 cm. Find the surface area to be coloure
The surface area to be coloured is 39.6 cm².
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed
The canal will irrigate an area of 562500 m² in 30 minutes.
A toy is in the shape of a cone mounted on a hemisphere, both of radius 7 cm. The total height of the toy is 21 cm. Find the volume of the toy. (Use π = 22/7.)
The volume of the toy is (4312)/(3) cm³ or approximately 1437.33 cm³.
A decorative block 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 di
The total surface area of the block is 163.86 cm².
Hello! I am your AI Math Tutor. Let's solve this problem step-by-step together. Let's start with Step 1! **Step 1: Visualize the cross-section** To solve this 3
The cross-section of a cone with an inscribed sphere is a triangle with an inscribed circle.
(a) The largest possible hemisphere is drilled out from a wooden cubical block of side 21 cm such that the base of the hemisphere is on one of the faces of the
(i) The volume of wood left in the block is 6835.5 cm³. (ii) The total surface area of the remaining solid is 2992.5 cm².
(a) A tent is in the shape of a right circular cylinder up to a height of 3 m and then a right circular cone, with a maximum height of 13.5 m above the ground.
The volume of the wooden toy is 266.112 cm³ and the total surface area of the toy is 207.996 cm².
A cap is cylindrical in shape, surmounted by a conical top. If the volume of the cylindrical part is equal to that of the conical part, then the ratio of the he
The ratio of the height of the cylindrical part to the height of the conical part is 1:3.
From a solid cone, whose height is 16 cm and radius 12 cm, and conical cavity of height 3 cm and base radius 4 cm is hollowed out such that the bases of the con
388π cm²
Assertion (A): If surface areas of the two spheres are in the ratio 16: 9, then their volumes are in the ratio 64: 27. Reason (R): If S_1 and S_2 are the surfac
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
A solid is hemispherical at the bottom and conical above (of same radius). If the curved surface areas of the two parts are equal, then the ratio of its radius
The ratio of its radius and the height of the conical part is 1:√3.
Given the three orthographic views of a solid as shown, find the volume of the solid.
The volume of the solid is (4√3)/(3) cubic units.
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine t
The volume of the toy is 25.12 cm³. The difference between the volumes of the cylinder and the toy is 25.12 cm³.
A juice seller was serving his customers using glasses as shown in Fig. 12.13. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass
The apparent capacity of the glass is 196.25 cm³ and its actual capacity is 163.542 cm³.
The decorative block shown in Fig. 12.7 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 fixe
The total surface area of the block is 163.86 cm².
A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. 12.8. The height of the entire rocket is 26 cm, while the height of the co
The area painted orange is 63.385 cm² and the area painted yellow is 195.465 cm².
Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped li
The area Rasheed has to colour is approximately 38.58 cm².

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