Question

(c)
A hemispherical and a conical hole is scooped out of a solid wooden cylinder.
Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and
cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number. Take n="/
cm...
7 cm​

Answer 1

The volume of remaining solid is 113 cm³

Step-by-step explanation:

A hemispherical and a conical hole is scooped out of a solid wooden cylinder.

Dimension of cylinder:-

Radius, r = 3 cm

Height, h = 7 cm

• Volume of cylinder, $V=\pi r^2h$

$V=\pi \cdot 3^2\cdot 7$

$V=63\pi\text{ cm}^3$

Dimension of cone:-

Radius, r = 3 cm

Height, h = 3 cm

• Volume of cone, $V=\dfrac{1}{3}\pi r^2h$

$V=\dfrac{1}{3}\cdot\pi \cdot 3^2\cdot 3$

$V=9\pi\text{ cm}^3$

Dimension of hemi-sphere:-

Radius, r = 3 cm

• Volume of hemi-sphere, $V=\dfrac{2}{3}\pi r^3$

$V=\dfrac{2}{3}\cdot\pi \cdot 3^3$

$V=18\pi\text{ cm}^3$

Volume of remaining solid = Volume cylinder - volume of cone - volume of hemi-sphere

Volume of remaining solid $=63\pi-9\pi-18\pi$

                                            $=36\pi\text{ cm}^3$

where, $\pi=3.14$

                                            $=36\cdot 3.14\approx 113\text{ cm}^3$

So, the remaining volume is 113 cm³

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