Maharashtra SSC Geometry HOTS Questions with Answers – Mensuration | Class 10 Board Exam 2027

Asked in: March 2026 board paper (same type with side 10 cm in July 2024 and side 2 cm in July 2025)

If the side of the cube is 5 cm, then the volume of that cube is ____ .

Asked in: March 2024 board paper (same type in July 2024 with r = 4 cm, l = 10 cm, and in June 2026 with r = 35 cm, l = 22 cm)

Radius of a sector of a circle is 3.5 cm and length of its arc is 2.2 cm. Find the area of the sector.

Asked in: March 2024 and July 2025 board papers (diameter 14 cm, i.e. the same sphere, in July 2024)

Find the surface area of a sphere of radius 7 cm.

Asked in: July 2024 board paper (same type with r = 7 cm, h = 15 cm in July 2025)

Complete the following activity to find the volume of a cone if the radius of its base is 7 cm and its perpendicular height is 6 cm.

Activity: Here, radius (r) = 7 cm, height (h) = 6 cm

\(\therefore\) Volume of cone = ____ (Formula)

\(= \dfrac{1}{3} \times \dfrac{22}{7} \times \text{____} \times 6\)

\(\therefore\) Volume of cone = ____ cm\(^3\)

Asked in: March 2024 board paper (square-minus-sector shaded region of the same kind in March 2026)

In the figure, □ABCD is a square and a circle is inscribed in it. All sides of the square touch the circle. If AB = 14 cm, find the area of the shaded region.

[Figure: Square ABCD of side 14 cm with a circle touching all four sides; the four corner regions outside the circle are shaded.]

Solution: Area of square = (____)\(^2\) (Formula) = \(14^2\) = ____ cm\(^2\)

Area of circle = ____ (Formula) \(= \dfrac{22}{7} \times 7 \times 7 = 154\) cm\(^2\)

(Area of shaded portion) = (Area of square) – (Area of circle) = 196 – 154 = ____ cm\(^2\)

Asked in: July 2024 board paper

A cylinder is having radius 7 cm and height 21 cm. Complete the following activity to calculate its volume and circumference of its base.

Activity: Radius (r) = 7 cm, Height (h) = 21 cm

Volume of cylinder = ____ (Formula) \(= \dfrac{22}{7} \times 7 \times 7 \times \text{____} = 154 \times 21 = \text{____}\) cm\(^3\)

Circumference of base = ____ (Formula) \(= 2 \times \dfrac{22}{7} \times \text{____} = \text{____}\) cm

Asked in: March 2025 board paper

How many solid cylinders of radius 10 cm and height 6 cm can be made by melting a solid sphere of radius 30 cm?

Asked in: June 2026 board paper

Find the number of coins of 2.2 cm diameter and 0.2 cm thick that can be made by melting a metallic right circular cylinder of height 0.2 m and diameter 8.8 cm.

Asked in: March 2024 board paper

A cylinder of radius 12 cm contains water up to the height 20 cm. A spherical iron ball is dropped into the cylinder and thus water level is raised by 6.75 cm. What is the radius of the iron ball?

Asked in: March 2025 board paper

The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum is 8 cm, find (\(\pi = 3.14\)):

(i) Curved surface area of frustum. (ii) Total surface area of the frustum. (iii) Volume of the frustum.

Asked in: March 2026 board paper (frustum also asked in March 2025)

A bucket is frustum shaped. Its height is 28 cm. Radii of circular faces are 12 cm and 15 cm. Find the capacity of the bucket in litres. \(\left(\pi = \dfrac{22}{7}\right)\)

Asked in: March 2026 board paper

Surface area of a sphere and total surface area of a cube are the same. Show that the ratio of the volume of the sphere to that of the cube is \(\sqrt6 : \sqrt\pi\).

The volume of a hemisphere of radius 3 cm is ____ .

The curved surface area of a cylinder of radius 7 cm and height 10 cm is ____ .

Find the length of an arc of a circle of radius 21 cm whose measure is 60°.

The radius of a cone is 6 cm and its perpendicular height is 8 cm. Find its slant height.

Find the total surface area of a solid hemisphere of radius 7 cm.

In a circle with centre O and radius 14 cm, chord AB subtends a right angle at the centre. Find the area of the minor segment cut off by chord AB.

The volume of a sphere is 38808 cm\(^3\). Find its radius. \(\left(\pi = \dfrac{22}{7}\right)\)

A toy is in the form of a cone mounted on a hemisphere of the same radius 3.5 cm. The total height of the toy is 15.5 cm. Find the volume of the toy. \(\left(\pi = \dfrac{22}{7}\right)\)

The radii of the two circular ends of a frustum are 20 cm and 12 cm and its height is 15 cm. Find its slant height and curved surface area. (\(\pi = 3.14\))

A metallic sphere of radius 6 cm is melted and drawn into a wire of radius 0.2 cm. Find the length of the wire.

The minute hand of a clock is 14 cm long. Find the area swept by it in 20 minutes and the distance travelled by its tip in that time. \(\left(\pi = \dfrac{22}{7}\right)\)

A cylindrical container of diameter 12 cm and height 15 cm is full of ice-cream. It is to be filled into cones of diameter 6 cm and height 12 cm, each with a hemispherical top of the same radius. How many such cones can be filled?

A tent is in the shape of a cylinder of diameter 14 m and height 3 m, surmounted by a cone of the same base whose slant height is 10 m. Find the area of canvas needed for the tent (floor not covered) and its cost at ₹ 50 per m\(^2\). \(\left(\pi = \dfrac{22}{7}\right)\)

The radius of a sphere is increased by 10%. Find the percentage increase in (i) its surface area and (ii) its volume.